The article describes the method of probabilistic reliability assessment of the ground bases constructions based on the adaptation of the regulatory assessment methodology and the use of the probability theory. In contrast to the standard (deterministic) methods, probabilistic assessment provides a quantitative expression of the reliability with the random nature of seismic effects and properties of soils. An analysis of the reliability index sensitivity to random changes in the parameters can be simultaneously performed, that reduces the number of random factors in the calculation of reliability. In this paper, the estimated base model is a semi-infinite homogeneous medium, but the described methods can be used for more complex models of soil bases. The method consists in adapting the relations used in the regulatory methodology to assess the reliability with the random nature of the values within the relations. This adaptation is realized by the construction of the model response function followed by Fourier series expansion and preservation of the linear terms in the expansion. Next, the apparatus of probability theory is used, which calculates the probability characteristics of the response function (the mean and variance). Subject to the requirements of a normal distribution of the original random variables obtained data allow us to compute probability of the reliable operation of the base.